There have been used power supply systems configured such that a chargeable and dischargeable secondary battery can supply a power to a load and the secondary battery can be charged even during an operation of the load when necessary. Typically, this kind of power supply systems are mounted on hybrid vehicles and electric vehicle that employ an electric motor driven by the secondary battery as a drive power source.
In this power supply system, an accumulated electric power of the secondary battery is used as a drive electric power of an electric motor that is a drive power source. Also, the secondary battery is charged with powers such as an electric power generated by regeneration of this electric motor and an electric power generated by an electric generator that generates the power according to rotation of an engine. In this kind of power supply system, a state estimating device of a secondary battery is typically required to obtain correctly an SOC (State Of Charge) with respect to a fully charged state. More specifically, it is necessary to restrict excessive charging and discharging of the secondary battery by successively and accurately estimating the SOC of the secondary battery even during the charging/discharging and immediately after the charging/discharging. Battery parameters (internal resistance and others) of the secondary battery gradually change and deteriorate with use so that it is required to estimate accurately the state of the secondary battery corresponding to the secular change.
For example, Japanese Patent Laying-Open No. 2003-075518 (which will be referred to as a “Patent Document 1”) has disclosed an SOC estimating device of a secondary battery in which parameters relating to a battery model represented as a linear equalization circuit is collectively or simultaneously estimated by applying an adaptive digital filter to the battery model, an internal battery resistance or a battery time constant is obtained from the estimated parameters, and a degree of the battery deterioration can be estimated based on prestored map data of the battery-internal resistance and the SOC or prestored map data of the battery time constant and the SOC.
In the SOC estimating device of the secondary battery disclosed in the Patent Document 1, as can be seen from FIG. 3 thereof, an RC parallel circuit formed of a resistance R1 representing a pure electric resistance, a charge-transfer resistance R2 and an electric double layer capacitance C1 is used as an equalization circuit model. In this equalization circuit model, changes in voltage caused by diffusion of a reaction-articipating material are approximately represented due a response delay caused by the RC parallel circuit so that it is practically difficult to achieve a sufficiently high accuracy with consideration given to the diffusion of the reaction-participating material inside the secondary battery.
In T. F. Fuller, M. Doyle and J. Newman “Simulation and Optimization of the Dual Lithium Ion Insertion Cell”, J. Electrochem. Soc., Vol. 141, No. 1 (1994), pp. 1-10 and W. B. Gu and C. Y. Wang “Thermal-Electrochemical Coupled Modeling of a Lithium-Ion Cell”, ECS Proceedings, Vol. 99-25 (1), 2000, pp. 748-762, which will be referred to as Non-Patent Documents 1 and 2, respectively, studies are made on cell models based on electrochemical reactions inside lithium-ion cells, and it is reported that cell characteristics can be precisely expressed by a comparison with actual cells. Particularly, Non-Patent Documents 1 and 2 have disclosed that an open-circuit voltage of a secondary battery depends on a local SOC at an electrolyte interface (active material surface), and consequently a battery voltage in a relaxation state is governed by diffusion of lithium that depends on a lithium concentration distribution in the active material. Particularly, the diffusion of the reaction-participating material (lithium) in the active material is governed by a diffusion equation of polar coordinates handling the active materials as spheres, and a diffusion rate of the material during a diffusion processing is governed by a diffusion coefficient.
In the battery model of the linear equalization circuit disclosed in the Patent Document 1, the changes in voltage due to diffusion of the reaction-participating material are approximately represented by the response delay due to the RC parallel circuit. Therefore, an RC ladder circuit formed of a series connection of a plurality of RC parallel circuits is required for obtaining a sufficiently high estimation accuracy expressing the actual diffusion process. However, when the RC ladder circuit is used as the equalization circuit model, the number of parameters to be estimated by the adaptive digital filter increases, which results in a problem of increase in arithmetic quantity and an insufficient estimation accuracy.
Further, in the Patent Document 1, the adaptive digital filter is used for estimating the battery parameters. However, the battery parameters significantly change depending on the battery states such as a battery temperature and an SOC. Therefore, it is preferable for estimating the degree of battery deterioration to estimate only the changes of parameters that change relatively slowly due to the secular change and thus have large time constants. However, it is actually configured to estimate also the changes of parameters that change relatively rapidly due to changes in battery state and thus have small time constants. For performing the estimation while following the battery parameters that change rapidly, therefore, it is necessary to take measures such that a device employs a plurality of open-circuit voltage estimating units having different arithmetic periods, respectively, and thereby inappropriate open-circuit voltage estimating units are successively initialized depending on the battery temperature. This results in a problem of increase in arithmetic quantity and storage capacitance. Further, when the battery parameters that change rapidly are estimated, such a problem Occur that a delay in estimation and a large estimation error due to noises or the like are liable to occur, and it may be impossible to ensure the state estimation accuracy of the battery model by appropriately updating the parameter values reflecting identification results and to execute appropriately the deterioration estimation based on the identification result values.
Further, in the Patent Document 1, the adaptive digital filter arithmetic is performed to estimate collectively the parameters of the battery model from the current and voltage, and the battery-internal resistance and time constant are obtained using the result of this estimation. However, when it is attempted to obtain simultaneously the battery-internal resistance and the time constant affected by the diffusion rate of the reaction-participating material, appropriate identification may be impossible. More specifically, the identification may be erroneously performed such that the battery-internal resistance has increased, in spite of the fact that the time constant has increased due to deterioration of the battery. Conversely, the identification may be erroneously performed such that the time constant has increased, in spite of the fact that the internal resistance has actually increased. Therefore, when the degree of battery deterioration is to be estimated based on the battery-internal resistance and the time constant obtained in the above manner, a deterioration determining method may become complicated for avoiding erroneous determination of the deterioration.
Conversely, in the Non-Patent Documents 1 and 2, the diffusion of the reaction-participating material is expressed by the diffusion equation based on the electrochemical reaction inside the battery, and it is considered that the open-circuit voltage of the battery depends on the local SOC in the electrode-electrolyte interface (active material surface). In this case, the battery model becomes nonlinear, but the battery-internal state can be estimated more accurately. However, for estimating the degree of battery deterioration using this battery model, the diffusion coefficient governing the diffusion of the reaction-participating material must be estimated together with DC resistance components such as a pure resistance and a charge-transfer resistance.
However, the adaptive digital filter disclosed in the Patent Document 1 cannot be applied to the nonlinear model as it is. A nonlinear adaptive digital filter (extended Karman filter or the like) that allows parameter identification can be applied to the nonlinear model, but this results in problems such as an extremely large quantity of arithmetic.